Fundamental Physical Constants

The fundamental physical constants used in MOPAC were updated in 1993 to conform with the 1986 CODATA recommendations [71]. The constants used in MOPAC are given in the Table. As a result of this update, all calculated quantities in MOPAC, except molecular weight, will change slightly when compared to earlier MOPACs (MOPAC 6 and earlier). Most of the time, changes in ΔHf are less than 0.1 kcal/mol. It is not anticipated that the physical constants will change again. If they do, however, the effect on calculated properties should be very small.

The derived quantities, AM, AD, AQ, EISOL, DD, and QQ are functions of the fundamental constants. Rather than change all of these, they are evaluated at the start of each calculation. This is a quick operation, taking only about 0.1s, and prevents any mistakes being introduced due to human error.

Table:
Fundamental Physical Constants

Physical Constant	Symbol	Value	Units
Speed of Light	c	299 792 458	m sec^-1 (Definition)
Planck constant	h	6.626 075 5(40) x10^-34	J sec
		6.626 075 5(40) x10^-27	erg s
Avogadro constant	N	6.022 136 7(36)x10²³	mol^-1
Molar gas constant	R	1.987 215 6	cal/mol/degree
		8.314 510(70)	J/mol/K
Volume of 1 mol of gas	V₀	22.414 10(19)	l/mol (at 1 atm, 25 C)
Electron volt	eV	1.602 177 33(49)x10^-19	J
Electron charge	e	1.602 177 33(49)x10^-19	C
Hartree	E_h	27.211 396 1(81)	eV
Electrostatic energy	E_ha_o	14.399 651 782 565	eV
Bohr radius	$a_{circ}$	0.529 177 249(24)x10^-10	m
Boltzmann constant	k = R/N	1.380 658(12)x10^-23	J/K
		1.380 658(12)x10^-16	erg/K
pi	π	3.141 592 653 589 79
Joule	J/cal	4.184	J/cal (Definition)
cm^-1	hc/eV	1.239 842 4x10^-4	eV
cm^-1	hcN/(1000J/cal)	2.859 144x10^-3	kcal/mol
cm^-1	hcN/(J/cal)	2.859 144	cal/mol
cm^-1		1.196 266x10⁸	erg = dyne Å^-1
Atomic unit (a.u.)		8.657 10x10^-33	e.s.u.
a.u.		2.541 747 8x10^-40	Debye
a.u.		51.422 082	V m^-1
kcal/mol		6.947 700x10^-13	erg
1 J		1.x10⁷	erg
1 eV		23.060 542 301 389	kcal/mol
1a.u.		627.509 6	kcal/mol
1 atm		1.013 25x10⁵	Pa
		1.013 25x10⁶	dyn/cm² (Definition)

Note: The precision of derived constants should not be used as an indication of their accuracy.
The uncertainty in the fundamental constants is given in parenthesis after the value.